| We first derive the conditions on a general gauge vector action for invariance under electromagnetic duality transformations using the Hamiltonian formulation. We then present the shock-free wave propagation requirements for various massless fields. First, we briefly argue how the "completely exceptional" approach, originally developed to study the characteristics of hyperbolic systems in 1 + 1 dimensions, can be generalized to higher dimensions and used to describe propagation without emerging shocks, with characteristic flow remaining parallel along the waves. We study the resulting requirements for scalar, vector, vector-scalar and gravity models and characterize physically acceptable actions in each case. Among the models of nonlinear electrodynamics we show that only Maxwell and Born-Infeld also obey duality invariance. Separately we show that, for actions depending only on the F2mn invariant, the permitted models have L∼1+F2. We characterize acceptable vector-scalar systems. We also find that wide classes of gravity models share with Einstein the null nature of their characteristic surfaces. Finally we give a brief review of recent developments in string theory and describe deformations of four dimensional N = 4 super-Yang-Mills theory which preserve N = 1 supersymmetry. |
